Solution of Vandermonde-Like Systems and Confluent Vandermonde-Like Systems
Hao Lu · SIAM Journal on Matrix Analysis and Applications · 1996
It is shown that the solution of Vandermonde-like systems and the solution of confluent Vandermonde-like systems can be obtained by evaluation of certain polynomials and Hermite evaluation of certain rational functions in terms of a J-match of polynomials, respectively. Based on these results, the existence of an $O( n \log^2 n )$ algorithm is shown for both Vandermonde-like systems and confluent Vandermonde-like systems for the case where the polynomials satisfy a three-term recurrence relation.